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I am not familiar with the change-of-variable technique that the question refers to. Does anyone have an idea what is meant and how one should go about doing it?

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rbm
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  • Note: this is not a homework question, but I'm studying for exams. – rbm Oct 21 '13 at 09:12
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    Most likely by the change-of-variables technique is meant the usual method involving Jacobians. However, the result that you are asked to prove is false unless the univariate standard normal random variables are independent random variables. See this answer for a great description of how two normal random variables can fail to have a bivariate normal distribution. – Dilip Sarwate Oct 21 '13 at 12:16
  • @DilipSarwate Thank you. I assume though that that is probably what the professor meant. Could you show me how the method with the Jacobians works assuming that that is so? – rbm Oct 21 '13 at 12:30
  • See this document for how the Jacobian method applies to the special case of linear transformations of normal random variables. – Dilip Sarwate Oct 21 '13 at 13:01
  • @DilipSarwate Hmmh, I still don't really understand how it would work in this case. Could you please show me? – rbm Oct 21 '13 at 17:02

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